New iTunes will not install

We use Mac OS X version 10.7.5

Our family has all updated to ios 7 and we can't get the new itunes working.

When I open itunes I get "A new version of ITunes (11.1.1) is avaible. etc.

So i start downloading it and go through all the terms and conditions and then it says

"Some of the selected updates couldn't be saved. "You don't have permission."

So i scrapped that idea and downloaded it from the apple website

I went through the terms and conditions again and the installation said

*** There were errors with the installation. You may want to try installing again.

The installion failed.

The installer can't create the folder " /var/folders/px/lynqqb595wvf1513g5nycwqw0000gq/T//Install.4799Hipr3N " ***

I've done this loads and it keeps saying the same thing, how do we fix it?!?!

Thanks:)